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Abstract: Given a topological space X, one can consider X endowed with many different geometric structures and the subgroup of the homeomorphism group of X that preserves that structure. For example, one might give X a differentiable structure and consider the group of diffeomorphisms of X. The question is: Do algebraic properties of the group of structure preserving automorphisms of X determine the structure? A question of this type is the following: Let M and N be two differentiable manifolds with groups of diffeomorphisms Diff (M) and Diff (N). Suppose there is a group isomorphism I: Diff (M)\to Diff (N). Is there a diffeomorphism f:M\to N such that I(g)=(f\circ g\circ f^{-1}) for all g \in Diff (M)? An affirmative answer implies in particular that M and N are diffeomorphic. In this talk, I will discuss the analogous question when X carries the structure of an orbifold. The talk will include relevant history, definitions and examples.
This talk will be accessible to graduate students.
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